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<p>Consider the following initial value problem</p>
<div class="displaymath process-math" data-contains-math-knowls="">
\begin{equation}
y^{\prime}+p(x)y=q(x), \quad y(x_0)=y_0.\tag{2.2.1}
\end{equation}
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<p class="continuation">There are several questions need to be answered:<span class="process-math">\((1)\)</span> Does there always exist a solution? (existence)<span class="process-math">\((2)\)</span> Is there only one solution? (Uniqueness)<span class="process-math">\((3)\)</span> Is the solution valid for all <span class="process-math">\(x\)</span> or for <span class="process-math">\(x\)</span> in certain interval?</p>
<span class="incontext"><a href="sec2_2.html#p-22" class="internal">in-context</a></span>
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